Archytas of Tarentum: Pythagorean, Philosopher and Mathematician King

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Cambridge University Press, 23 mag 2005
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Archytas of Tarentum is one of the three most important philosophers in the Pythagorean tradition, a prominent mathematician, who gave the first solution to the famous problem of doubling the cube, an important music theorist, and the leader of a powerful Greek city-state. He is famous for sending a trireme to rescue Plato from the clutches of the tyrant of Syracuse, Dionysius II, in 361 BC. This 2005 study was the first extensive enquiry into Archytas' work in any language. It contains original texts, English translations and a commentary for all the fragments of his writings and for all testimonia concerning his life and work. In addition there are introductory essays on Archytas' life and writings, his philosophy, and the question of authenticity. Carl A. Huffman presents an interpretation of Archytas' significance both for the Pythagorean tradition and also for fourth-century Greek thought, including the philosophies of Plato and Aristotle.

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Indice

Life writings and reception
3
The philosophy of Archytas
44
The authenticity question
91
Fragment 1
103
Fragment 1
162
Testimonia for Archytas life writings
255
Moral philosophy and character
283
The duplication of the cube A14 and A15
342
Metaphysics
483
Physics
508
The argument to show that the cosmos is unlimited A24
540
Miscellaneous testimonia
570
Spurious writings and testimonia
595
Archytas name
619
Select index of Greek words and phrases
638
General index
651

Music
402

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Pagina 270 - Sunt ista ut dicis; sed audisse te credo Tubero, Platonem Socrate mortuo primum in Aegyptum discendi causa, post in Italiam et in Siciliam contendisse, ut Pythagorae inventa perdisceret...
Pagina 270 - Quare 87 hoc videndum est, possitue nobis hoc ratio philo30 sophorum dare. Pollicetur certe. Nisi enim id faceret, cur Plato Aegyptum peragravit, ut a sacerdotibus barbaris numeros et caelestia acciperet? cur post Tarentum ad Archytam? cur ad reliquos Pythagoreos, Echecratem , Timaeum , Arionem Locros , ut , cum к Socratem expressisset , adiungeret Pythagoreorum disciplinam eaque, quae Socrates repudiabat, addisceret?
Pagina 123 - For it is clear that these studies are like ladders and bridges that carry our minds from things apprehended by sense and opinion to those comprehended by the mind and understanding, and from those material, physical things, our foster-brethren known to us from childhood, to the things with which we are unacquainted, foreign to our senses, but in their immateriality and eternity more akin to our souls, and above all to the reason which is in our souls.
Pagina 257 - But those individuals bus vero natura tantum tribuit sollertiae, acuminis, memoriae, ut possint geometriam, astrologiam, musicen ceterasque disciplinas penitus habere notas, praetereunt officia architectorum et efficiuntur mathematici. Itaque faciliter contra eas disciplinas disputare possunt, quod pluribus telis disciplinarum sunt armati. Hi autem inveniuntur raro, ut aliquando fuerunt Aristarchus Samius, Philolaus et Archytas Tarentini, Apollonius Pergaeus, Eratosthenes Cyrenaeus, Archimedes et...
Pagina 271 - Ш vit, unde proficeret, et ad Pythagorae disciplinam se contulit. quam etsi ratione diligenti et magnifica instructam videbat, rerum tamen continentiam et castitatem magis cupiebat imitari et, quod Pythagoreorum ingenium adiutum disciplinis aliis sentiebat, ad Theodorum Cyrenas , ut geometriam disce- 10 ret, est profectus et astrologiam adusque Aegyptum ivit petitum, ut inde prophetarum etiam ritus addisceret.
Pagina 263 - Apollo ; poscis ab invita verba pigenda lyra. certa feram certis auctoribus, aut ego vates nescius aerata signa movere pila.
Pagina 358 - And this he proved by showing that the squares on the diameters have the same ratios as the...
Pagina 151 - I formed my judgments, learning from the common nature of all and the particular nature of the individual, from the disease, the patient, the regimen prescribed and the prescriber — for these make a diagnosis more...
Pagina 257 - Hence they can readily take up positions against those arts because many are the artistic weapons with which they are armed. Such men, however, are rarely found, but there have been such at times; for example, Aristarchus of Samos, Philolaus and Archytas of Tarentum, Apollonius of Perga, Eratosthenes of Cyrene...
Pagina 465 - PROPOSITION 8 If between two numbers there fall numbers in continued proportion with them, then, however many numbers fall between them in continued proportion, so many will also fall in continued proportion between the numbers which have the same ratio with the original numbers.

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